In recent years, a straddle electric vehicle which incorporates as a driving power source an electric motor activated by electric energy stored in a battery has been developed. In the straddle electric vehicle, it is considered that the battery is repeatedly charged and discharged with a current of a great magnitude in response to the acceleration/deceleration operation of the electric motor for moving a vehicle body and thereby generates heat, and therefore it is necessary to appropriately cool the battery. The battery may be exposed to the outside to be cooled by ram air. However, if the battery is seen from the outside, its external appearance is not good. If possible, the battery is covered with a case. Under the circumstances, a configuration is proposed, in which the battery is covered with a battery case, and ram air is introduced into a battery cover through a ram air inlet provided at the lower side of the battery case to cool the battery (see e.g., Patent Literature 1).